OFFSET
1,2
COMMENTS
A003172 is the main entry for this sequence, which removes duplicates (i.e., for nonsquarefree n) like Q(sqrt(8)) = Q(sqrt(2)).
See A146209 for the complement (without nonsquarefree numbers like 40, ...) {10, 15, 26, 30, 34, 35, 39, 42, 51, 55, 58, 65, 66, 70, 74, 78, 79, ...} (supersequence of A029702, A053330 and A051990). - M. F. Hasler, Oct 30 2014
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
The following are in this sequence:
1, 4, 9, 16, ... because Z is a UFD (by the Fundamental Theorem of Arithmetic);
2, 8, 18, 32, ... because Z[sqrt(2)] has unique factorization;
3, 12, 27, 48, ... because Z[(1+sqrt(3))/2] has unique factorization;
5, 20, 45, 80, ... because Z[(1+sqrt(5))/2] has unique factorization.
MATHEMATICA
Select[Range[100], NumberFieldClassNumber[Sqrt[#]] == 1 &] (* Alonso del Arte, Feb 19 2013 *)
PROG
(PARI) is(n)=n=core(n); n==1 || !#bnfinit('x^2-n).cyc
CROSSREFS
KEYWORD
nonn
AUTHOR
Charles R Greathouse IV, Feb 19 2013
STATUS
approved